## Optimisation

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EduardK
Posts: 1
Joined: Wed Feb 12, 2020 2:14 pm
First Name: Eduard
Last Name: Kas

### Optimisation

In the attached simple 'airline business model' I tried to determine the optimal combination of ticket price ('fare') and number of airplanes. The suggested solution of a fare of \$282.4 and the use of 4 airplanes does not appear to optimal, given that for the predicted demand at this price 2 airplanes would suffice. (In accordance with the assumed relationship between the ticket price and demand, a price of \$282.4 would translate into a demand of 283,000 seats and given an annual capacity of 144,000 seats per plane 2 planes would suffice.)

My basic question is : what am I doing wrong? I am missing something?

Further explanation of the airline business model: There is a connection between demand and annual capacity. The number of seats sold may equal the demand if demand is equal or less than the annual capacity. (I write here 'may', because depending on the ticket price, it might be more economical to sell less tickets than could be sold. For example, when the demand equals 2.4 times the annual capacity of a plane, at one ticket price it might be optimal to sell only the number of tickets to satisfy the demand that equals the annual capacity of 2 planes. At a higher ticket price, it might be optimal to satisfy all of the demand and use 3 planes.) If demand exceeds the annual capacity, then the number of seats sold equals the annual capacity. See the block 'Seats sold'.

In the model the ticket price lies between the minimum of \$100 and the maximum of \$400 per seat, while the airline company uses in between 1 and 5 planes.

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